Threshold value of the penalty parameter in the minimization of $L_1$-penalized conditional value-at-risk | Zendy

Vladimir Gaitsgory | Zendy; Tanya Tarnopolskaya | Zendy

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Threshold value of the penalty parameter in the minimization of $L_1$-penalized conditional value-at-risk

Author(s) -

Vladimir Gaitsgory,

Tanya Tarnopolskaya

Publication year - 2012

Publication title -

journal of industrial and management optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.325

H-Index - 32

eISSN - 1553-166X

pISSN - 1547-5816

DOI - 10.3934/jimo.2013.9.191

Subject(s) - cvar , value (mathematics) , minification , mathematical optimization , mathematics , bounded function , penalty method , expected shortfall , statistics , economics , risk management , mathematical analysis , management

A problem of minimization of L₁-penalized conditional value-at-risk (CVaR) is considered. It is shown that there exists a non-negative threshold value of the penalty parameter such that the optimal value of the penalized problem is unbounded if the penalty parameter is less than the threshold value, and it is bounded if the penalty parameter is greater or equal than this value. It is established that the threshold value can be found via the solution of a linear programming problem, and, therefore, readily computable. Theoretical results are illustrated by numerical examples.14 page(s

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